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This thesis attempts to test several frameworks of non-Newtonian gravity in the context of galaxies and galaxy clusters. The theory most extensively discussed was that of Modiﬁed Newtonian Dynamics (MOND) with Galileon gravity, Emergent Gravity (EG) and Modiﬁed Gravity (MOG) mentioned to a lesser extent. Speciﬁcally, the main focus of this thesis was to determine whether MOND and MOND-like theories were compatible with galaxy cluster data, without the need to include cold dark matter. To do this, the paradigms of Extended MOND (EMOND), Generalised MOND (GMOND) and superﬂuid dark matter were investigated. The theories were outlined and applied to galaxy cluster data. The main ﬁndings of this were that EMOND and GMOND had some success with explaining galaxy cluster mass proﬁles, without requiring an additional dark matter component. The superﬂuid paradigm also enjoyed some success in galaxy clusters, which was expected as it behaves in a similar manner to the standard cold dark matter paradigm in cluster environments. However, the superﬂuid paradigm may have issues in the very centre of galaxy clusters due to the theory predicting constant density cores, whereas the cold dark matter paradigm predicts density cores which are cuspier.
The EMOND paradigm was also tested against ultra-diffuse galaxy (UDGs) data as they appear in cluster environments, where EMOND becomes important. It was found that EMOND can reproduce the inferred mass of the UDGs, assuming they lie on the fundamental manifold (FM). The validity of the assumptions used to model the UDGs are discussed in the text.
A two-body problem was also conducted in the Galileon gravity framework. The amount of additional gravitational force, compared to Newtonian was determined for a small galaxy at the edge of a galaxy cluster.